Geodesic
The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 58-85

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We explore the implications of the possibility of decomposition of any TU game $v$ into the difference of two convex games $v_1$ and $v_2$, i.e. $v=v_1-v_2.$ In particular, we prove that the Shapley value of a game $v$ is the difference of the Steiner points of the cores $C(v_1)$ and $C(v_2),$ and, in particular, for a convex game $v$ the Shapley value is the Steiner point of its core. Some properties of this interpretation are studied. A new definition of the Weber set of a TU game is considered.
Keywords: TU games, convex games, the Shapley value, the Steiner point, differences of the cores. 
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     author = {Sergei L. Pechersky},
     title = {The {Shapley} value of {TU} games, differences of the cores of convex games, and the {Steiner} point of convex compact sets},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {58--85},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
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Sergei L. Pechersky. The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 58-85. http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a4/